Question: All of the 5th grade teachers and students from Almond went on a field trip to an art museum. Tickets were $$8.00$ each for teachers and $$4.50$ each for students, and the group paid $$60.00$ in total. The next month, the same group visited a natural history museum where the tickets cost $$16.00$ each for teachers and $$10.50$ each for students, and the group paid $$132.00$ in total. Find the number of teachers and students on the field trips.
Explanation: Let $x$ equal the number of teachers and $y$ equal the number of students. The system of equations is: ${8x+4.5y = 60}$ ${16x+10.5y = 132}$ Solve for $x$ and $y$ using elimination. Multiply the top equation by $-2$ ${-16x-9y = -120}$ ${16x+10.5y = 132}$ Add the top and bottom equations together. $ 1.5y = 12 $ $ y = \dfrac{12}{1.5}$ ${y = 8}$ Now that you know ${y = 8}$ , plug it back into $ {8x+4.5y = 60}$ to find $x$ ${8x + 4.5}{(8)}{= 60}$ $8x+36 = 60$ $8x = 24$ $x = \dfrac{24}{8}$ ${x = 3}$ You can also plug ${y = 8}$ into $ {16x+10.5y = 132}$ and get the same answer for $x$ ${16x + 10.5}{(8)}{= 132}$ ${x = 3}$ There were $3$ teachers and $8$ students on the field trips.